Stone-Wales defects preserve hyperuniformity in amorphous two-dimensional networks

Universal Hyperuniform Organization in Looped Leaf Vein Networks

The leaf vein network is a hierarchical vascular system that transports water and nutrients to the leaf cells. The thick primary veins form a branched network, while the secondary veins can develop closed loops forming a well-defined cellular structure. Through extensive analysis of a variety of distinct leaf species, we discover that the apparently disordered cellular structures of the secondary vein networks exhibit a universal hyperuniform organization and possess a hidden order on large scales. Disorder hyperuniform systems lack conventional long-range order, yet they completely suppress normalized infinite-wavelength density fluctuations like crystals. Specifically, we find that the distributions of the geometric centers associated with the vein network loops possess a vanishing static structure factor in the limit that the wave number k goes to 0, i.e., S(k)∼k^{α}, where α≈0.64±0.021, providing an example of class III hyperuniformity in biology. This hyperuniform organization leads to superior efficiency of diffusive transport, as evidenced by the much faster convergence of the time-dependent spreadability S(t) to its longtime asymptotic limit, compared to that of other uncorrelated or correlated disordered but nonhyperuniform organizations. Our results also have implications for the discovery and design of novel disordered network materials with optimal transport properties.

Nonequilibrium hyperuniform states in active turbulence

We demonstrate that the complex spatiotemporal structure in active fluids can feature characteristics of hyperuniformity. Using a hydrodynamic model, we show that the transition from hyperuniformity to nonhyperuniformity and antihyperuniformity depends on the strength of active forcing and can be related to features of active turbulence without and with scaling characteristics of inertial turbulence. Combined with identified signatures of Levy walks and nonuniversal diffusion in these systems, this allows for a biological interpretation and the speculation of nonequilibrium hyperuniform states in active fluids as optimal states with respect to robustness and strategies of evasion and foraging.

Vibrational properties of disordered stealthy hyperuniform 1D atomic chains

Disorder hyperuniformity is a recently discovered exotic state of many-body systems that possess a hidden order in between that of a perfect crystal and a completely disordered system. Recently, this novel disordered state has been observed in a number of quantum materials including amorphous 2D graphene and silica, which are endowed with unexpected electronic transport properties. Here, we numerically investigate 1D atomic chain models, including perfect crystalline, disordered stealthy hyperuniform (SHU) as well as randomly perturbed atom packing configurations to obtain a quantitative understanding of how the unique SHU disorder affects the vibrational properties of these low-dimensional materials. We find that the disordered SHU chains possess lower cohesive energies compared to the randomly perturbed chains, implying their potential reliability in experiments. Our inverse partition ratio (IPR) calculations indicate that the SHU chains can support fully delocalized states just like perfect crystalline chains over a wide range of frequencies, i.e.ω∈(0,100)cm-1, suggesting superior phonon transport behaviors within these frequencies, which was traditionally considered impossible in disordered systems. Interestingly, we observe the emergence of a group of highly localized states associated withω∼200cm-1, which is characterized by a significant peak in the IPR and a peak in phonon density of states at the corresponding frequency, and is potentially useful for decoupling electron and phonon degrees of freedom. These unique properties of disordered SHU chains have implications in the design and engineering of novel quantum materials for thermal and phononic applications.

Computational design of anisotropic stealthy hyperuniform composites with engineered directional scattering properties

Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)1359-645410.1016/j.actamat.2017.09.053] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function χ[over ̃]_{_{V}}(k) of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with χ[over ̃]_{_{V}}(k)=0 for k∈Ω, i.e., complete suppression of scattering in an "exclusion" region Ω around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of Ω lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions impose strong constraints on the global symmetry of the resulting media, they can still possess structures at a local level that are nearly isotropic. Both the isotropic and anisotropic hyperuniform microstructures associated with the elliptical-disk, square, and rectangular Ω possess phase-inversion symmetry over certain range of volume fractions and a percolation threshold ϕ_{c}≈0.5. On the other hand, the directionally hyperuniform microstructures associated with the butterfly-shaped and lemniscate-shaped Ω do not possess phase-inversion symmetry and percolate along certain directions at much lower volume fractions. We also apply our general procedure to construct stealthy nonhyperuniform systems. Our construction algorithm enables one to control the statistical anisotropy of composite microstructures via the shape, size, and symmetries of Ω, which is crucial to engineering directional optical, transport, and mechanical properties of two-phase composite media.

Novel Isomer of Volleyballene Sc20C60

The Stone-Wales defect is a well-known and significant defective structure in carbon materials, impacting their mechanical, chemical, and electronic properties. Recently, a novel metal-carbon nanomaterial named Volleyballene was discovered, characterized by a C-C bond bridging two carbon pentagons. Using first-principles calculations, a stable Stone-Wales-defective counterpart of Volleyballene, exhibiting Th symmetry, has been proposed by rotating the C-C bond by 90°. Although its binding energy per atom is slightly higher than that of Volleyballene (ΔEb = 0.009 eV/atom), implying marginally lower structural stability, it can maintain its bond structure until the effective temperature reaches about 1500 K, indicating greater thermodynamic stability. Additionally, its highest vibration frequency is 1346.2 cm-1, indicating a strong chemical bond strength. A theoretical analysis of the Sc20C60 + Sc20C60 binary systems highlights that the stable building block may be applied in potential nanoassemblies.

Finite-size effects in the static structure factor S(k) and S(0) for a two-dimensional Yukawa liquid

Finite-size effects in the static structure factor S(k) are analyzed for an amorphous substance. As the number of particles is reduced, S(0) increases greatly, up to an order of magnitude. Meanwhile, there is a decrease in the height of the first peak S_{peak}. These finite-size effects are modeled accurately by the Binder formula for S(0) and our empirical formula for S_{peak}. Procedures are suggested to correct for finite-size effects in S(k) data and in the hyperuniformity index H≡S(0)/S_{peak}. These principles generally apply to S(k) obtained from particle positions in noncrystalline substances. The amorphous substance we simulate is a two-dimensional liquid, with a soft Yukawa interaction modeling a dusty plasma experiment.

Crumpling Defective Graphene Sheets

Upon crumpling, graphene sheets yield intriguing hierarchical structures with high resistance to compression and aggregation, garnering a great deal of attention in recent years for their remarkable potential in a variety of applications. Here, we aim to understand the effect of Stone-Wales (SW) defects, i.e., a typical topological defect of graphene, on the crumpling behavior of graphene sheets at a fundamental level. By employing atomistically informed coarse-grained molecular dynamics (CG-MD) simulations, we find that SW defects strongly influence the sheet conformation as manifested by the change in size scaling laws and weaken the self-adhesion of the sheet during the crumpling process. Remarkably, the analyses of the internal structures (i.e., local curvatures, stresses, and cross-section patterns) of crumpled graphene emphasize the enhanced mechanical heterogeneity and "glass-like" amorphous state elicited by SW defects. Our findings pave the way for understanding and exploring the tailored design of crumpled structure via defect engineering.

Equilibrium states corresponding to targeted hyperuniform nonequilibrium pair statistics

The Zhang-Torquato conjecture [G. Zhang and S. Torquato, Phys. Rev. E, 2020, 101, 032124.] states that any realizable pair correlation function g₂(r) or structure factor S(k) of a translationally invariant nonequilibrium system can be attained by an equilibrium ensemble involving only (up to) effective two-body interactions. To further test and study this conjecture, we consider two singular nonequilibrium models of recent interest that also have the exotic hyperuniformity property: a 2D "perfect glass" and a 3D critical absorbing-state model. We find that each nonequilibrium target can be achieved accurately by equilibrium states with effective one- and two-body potentials, lending further support to the conjecture. To characterize the structural degeneracy of such a nonequilibrium-equilibrium correspondence, we compute higher-order statistics for both models, as well as those for a hyperuniform 3D uniformly randomized lattice (URL), whose higher-order statistics can be very precisely ascertained. Interestingly, we find that the differences in the higher-order statistics between nonequilibrium and equilibrium systems with matching pair statistics, as measured by the "hole" probability distribution, provide measures of the degree to which a system is out of equilibrium. We show that all three systems studied possess the bounded-hole property and that holes near the maximum hole size in the URL are much rarer than those in the underlying simple cubic lattice. Remarkably, upon quenching, the effective potentials for all three systems possess local energy minima (i.e., inherent structures) with stronger forms of hyperuniformity compared to their target counterparts. Our methods are expected to facilitate the self-assembly of tunable hyperuniform soft-matter systems.

Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids

Especially small values of the static structure factor S(k) at long wavelengths, i.e., small k, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of S(k) data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of S(k) at small k is typically in a range 0.02-0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that S(k) at small k generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of S(0), so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

Topological Stone-Wales Defects Enhance Bonding and Electronic Coupling at the Graphene/Metal Interface

Defects play a critical role for the functionality and performance of materials, but the understanding of the related effects is often lacking, because the typically low concentrations of defects make them difficult to study. A prominent case is the topological defects in two-dimensional materials such as graphene. The performance of graphene-based (opto-)electronic devices depends critically on the properties of the graphene/metal interfaces at the contacting electrodes. The question of how these interface properties depend on the ubiquitous topological defects in graphene is of high practical relevance, but could not be answered so far. Here, we focus on the prototypical Stone-Wales (S-W) topological defect and combine theoretical analysis with experimental investigations of molecular model systems. We show that the embedded defects undergo enhanced bonding and electron transfer with a copper surface, compared to regular graphene. These findings are experimentally corroborated using molecular models, where azupyrene mimics the S-W defect, while its isomer pyrene represents the ideal graphene structure. Experimental interaction energies, electronic-structure analysis, and adsorption distance differences confirm the defect-controlled bonding quantitatively. Our study reveals the important role of defects for the electronic coupling at graphene/metal interfaces and suggests that topological defect engineering can be used for performance control.

Two-Dimensional Ultrathin Silica Films

Two-dimensional (2D) ultrathin silica films have the potential to reach technological importance in electronics and catalysis. Several well-defined 2D-silica structures have been synthesized so far. The silica bilayer represents a 2D material with SiO₂ stoichiometry. It consists of precisely two layers of tetrahedral [SiO₄] building blocks, corner connected via oxygen bridges, thus forming a self-saturated silicon dioxide sheet with a thickness of ∼0.5 nm. Inspired by recent successful preparations and characterizations of these 2D-silica model systems, scientists now can forge novel concepts for realistic systems, particularly by atomic-scale studies with the most powerful and advanced surface science techniques and density functional theory calculations. This Review provides a solid introduction to these recent developments, breakthroughs, and implications on ultrathin 2D-silica films, including their atomic/electronic structures, chemical modifications, atom/molecule adsorptions, and catalytic reactivity properties, which can help to stimulate further investigations and understandings of these fundamentally important 2D materials.

Steady-like topology of the dynamical hydrogen bond network in supercooled water

We investigate the link between topology of the hydrogen bond network (HBN) and large-scale density fluctuations in water from ambient conditions to the glassy state. We observe a transition from a temperature-dependent topology at high temperatures, to a steady-like topology below the Widom temperature T_W ∼ 220 K signaling the fragile-to-strong crossover and the maximum in structural fluctuations. As a consequence of the steady topology, the network suppresses large-scale density fluctuations much more efficiently than at higher temperatures. Below T_W , the contribution of coordination defects of the kind A ₂ D ₁ (two acceptors and one donor) to the kinetics of the HBN becomes progressively more pronounced, suggesting that A ₂ D ₁ configurations may represent the main source of dynamical heterogeneities. Below the vitrification temperature, the freezing of rotational and translational degrees of freedom allow for an enhanced suppression of large-scale density fluctuations and the sample reaches the edges of nearly hyperuniformity. The formed network still hosts coordination defects, hence implying that nearly hyperuniformity goes beyond the classical continuous random network paradigm of tetrahedral networks and can emerge in scenarios much more complex than previously assumed. Our results unveil a hitherto undisclosed link between network topology and properties of water essential for better understanding water's rich and complex nature. Beyond implications for water, our findings pave the way to a better understanding of the physics of supercooled liquids and disordered hyperuniform networks at large.

Hyperuniform Active Chiral Fluids with Tunable Internal Structure

Large density fluctuations observed in active systems and hyperuniformity are two seemingly incompatible phenomena. However, the formation of hyperuniform states has been recently predicted in nonequilibrium fluids formed by chiral particles performing circular motion with the same handedness. Here we report evidence of hyperuniformity realized in a chiral active fluid comprised of pear-shaped Quincke rollers of arbitrary handedness. We show that hyperuniformity and large density fluctuations, triggered by dynamic clustering, coexist in this system at different length scales. The system loses its hyperuniformity as the curvature of particles' motion increases, transforming them into localized spinners. Our results experimentally demonstrate a novel hyperuniform active fluid and provide new insights into an interplay between chirality, activity, and hyperuniformity.

Ultraefficient reconstruction of effectively hyperuniform disordered biphase materials via non-Gaussian random fields

Disordered hyperuniform systems are statistically isotropic and possess no Bragg peaks like liquids and glasses, yet they suppress large-scale density fluctuations in a similar manner as in perfect crystals. The unique hyperuniform long-range order in these systems endow them with nearly optimal transport, electronic, and mechanical properties. The concept of hyperuniformity was originally introduced for many-particle systems and has subsequently been generalized to biphase heterogeneous materials such as porous media, composites, polymers, and biological tissues for unconventional property discovery. Existing methods for rendering realizations of disordered hyperuniform biphase materials reconstruction typically employ stochastic optimization such as the simulated annealing approach, which requires many iterations. Here, we propose an explicit ultraefficient method for reconstructing effectively hyperuniform biphase materials, based on the second-order non-Gaussian random fields where no additional tuning step or iteration is needed. Both the effectively hyperuniform microstructure and the latent material property field can be simultaneously generated in a single reconstruction. Moreover, our method can also incorporate hierarchical uncertainties in the heterogeneous materials, including both uncertainties in the disordered material microstructure and material property variation within each phase. The efficiency and feasibility of the proposed reconstruction method are demonstrated via a wide spectrum of examples spanning from isotropic to anisotropic, effectively hyperuniform to nonhyperuniform, and antihyperuniform systems. Our ultraefficient reconstruction method can be readily incorporated into material design, probabilistic analysis, optimization, and discovery of novel disordered hyperuniform heterogeneous materials.

Structural Amorphization-Induced Topological Order

Electronic properties of crystals are inherently pertained to crystalline symmetry, so that amorphization that lowers and breaks symmetry is detrimental. One important crystalline property is electron band topology which is known to be weakened and destroyed by structural disorder. Here, we report a counterintuitive theoretical discovery that atomic structural disorder by amorphization can in fact induce electronic order of topology in an otherwise topologically trivial crystal. The resulting nontrivial topology is characterized by a nonzero spin Bott index, associated with robust topological edge states and quantized conductance. The underlying topological phase transition (TPT) from a trivial crystal to a topological amorphous is analyzed by mapping out a phase diagram in the degree of structural disorder using an effective medium theory. The atomic disorder is revealed to induce topological order by renormalizing the spectral gap toward nontriviality near the phase boundary. As a concrete example, we further show such TPT in amorphous stanane by first-principles calculations. Our findings point to possible observation of an electronic ordering transition accompanied by a structural disorder transition.

Optoelectronic Current through Unbiased Monolayer Amorphous Carbon Nanojunctions

Monolayer amorphous carbon (MAC) is a recently synthesized disordered 2D carbon material. An ensemble of MAC nanofragments contains diverse manifestations of lattice disorder, and because of disorder the key unifying characteristic of this ensemble is poor electronic conductance. Curiously, our computational analysis of the electronic properties of MAC nanofragments revealed an additional commonality: a robust presence of charge-transfer character for electronic transitions from the occupied to virtual orbitals. This charge-transfer property suggests possible applications in optoelectronics. In this Letter, we demonstrate computationally that a laser pulse induces directional electronic currents in unbiased MAC nanojunctions and discuss the effects of pulse intensity on the magnitude of electron transfer.

Self-assembly of two-dimensional, amorphous materials on a liquid substrate

Recent experimental utilization of liquid substrate in the production of two-dimensional crystals, such as graphene, together with a general interest in amorphous materials, raises the following question: is it beneficial to use a liquid substrate to optimize amorphous material production? Inspired by epitaxial growth, we use a two-dimensional coarse-grained model of interacting particles to show that introducing a motion for the substrate atoms improves the self-assembly process of particles that move on top of the substrate. We find that a specific amount of substrate liquidity (for a given sample temperature) is needed to achieve optimal self-assembly. Our results illustrate the opportunities that the combination of different degrees of freedom provides to the self-assembly processes.

Diffusion spreadability as a probe of the microstructure of complex media across length scales

Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering, and biology. Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, S(t), which we call the spreadability, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for S(t) in any Euclidean space dimension d in terms of the autocovariance function as well as corresponding Fourier representations of S(t) in terms of the spectral density, which are especially useful when scattering information is available experimentally or theoretically. These are singular results because they are rare examples of mass transport problems where exact solutions are possible. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of S(t) enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the "excess" spreadability, S(∞)-S(t), decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the "slowest" being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. We obtain exact results for S(t) for a variety of specific ordered and disordered model microstructures across dimensions that span from hyperuniform to antihyperuniform media. Moreover, we establish a remarkable connection between the spreadability and an outstanding problem in discrete geometry, namely, microstructures with "fast" spreadabilities are also those that can be derived from efficient "coverings" of space. We also identify heretofore unnoticed, to our best knowledge, remarkable links between the spreadability S(t) and NMR pulsed field gradient spin-echo amplitude as well as diffusion MRI measurements. This investigation reveals that the time-dependent spreadability is a powerful, dynamic-based figure of merit to probe and classify the spectrum of possible microstructures of two-phase media across length scales.